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Scaling in the dynamical properties of complex many-body systems has been ofstrong interest since turbulence phenomena became the subject of systematicmathematical studies. In this article, dynamical critical phenomena far fromequilibrium are investigated with functional renormalisation group equations.The focus is set on scaling solutions of the stochastic driven-dissipativeBurgers equation and their relation to solutions known in the literature forBurgers and Kardar-Parisi-Zhang dynamics. We furthermore relate superfluid aswell as acoustic turbulence described by the Gross-Pitaevskii model to knownanalytic and numerical results for scaling solutions. In this way, thecanonical Kolmogorov exponent 5/3 for the energy cascade in superfluidturbulence is obtained analytically. We also get first results for anomalousexponents of acoustic and quantum turbulence. These are consistent withexisting experimental data. Our results should be relevant for futureexperiments with, e.g., exciton-polariton condensates in solid-state systems aswell as with ultra-cold atomic gases.

Anomalous scaling at non-thermal fixed points of Burgers' and Gross-Pitaevskii turbulence